Such a dosing device is generally known for pharmaceutical or cosmetic media such as liquids, gels, etc. The known dosing device is firmly connected to a medium reservoir by means of a casing part, which is provided with a closing cap. The dosing device has a pumping device in the form of a manually operable thrust piston pump. With the thrust piston pump is associated an applicator constructed as a nose olive provided with a finger support for the manual operation of the pumping device.